{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayesian Data Analysis, 3rd ed\n",
    "##  Chapter 5, demo 1\n",
    "\n",
    "Hierarchical model for Rats experiment (BDA3, p. 102)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import beta\n",
    "from scipy.special import gammaln\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import os, sys\n",
    "# add utilities directory to path\n",
    "util_path = os.path.abspath(os.path.join(os.path.pardir, 'utilities_and_data'))\n",
    "if util_path not in sys.path and os.path.exists(util_path):\n",
    "    sys.path.insert(0, util_path)\n",
    "\n",
    "# import from utilities\n",
    "import plot_tools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# edit default plot settings\n",
    "plt.rc('font', size=12)\n",
    "# apply custom background plotting style\n",
    "plt.style.use(plot_tools.custom_styles['gray_background'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# rat data (BDA3, p. 102)\n",
    "y = np.array([\n",
    "     0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  1,  1,  1,\n",
    "     1,  1,  1,  1,  1,  2,  2,  2,  2,  2,  2,  2,  2,  2,  1,  5,  2,\n",
    "     5,  3,  2,  7,  7,  3,  3,  2,  9, 10,  4,  4,  4,  4,  4,  4,  4,\n",
    "    10,  4,  4,  4,  5, 11, 12,  5,  5,  6,  5,  6,  6,  6,  6, 16, 15,\n",
    "    15,  9,  4\n",
    "])\n",
    "n = np.array([\n",
    "    20, 20, 20, 20, 20, 20, 20, 19, 19, 19, 19, 18, 18, 17, 20, 20, 20,\n",
    "    20, 19, 19, 18, 18, 25, 24, 23, 20, 20, 20, 20, 20, 20, 10, 49, 19,\n",
    "    46, 27, 17, 49, 47, 20, 20, 13, 48, 50, 20, 20, 20, 20, 20, 20, 20,\n",
    "    48, 19, 19, 19, 22, 46, 49, 20, 20, 23, 19, 22, 20, 20, 20, 52, 46,\n",
    "    47, 24, 14\n",
    "])\n",
    "M = len(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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qfpvQDIwMQAHv7ao4Y/c4XNFEQXULc0dEHvc8g05xx/QEvj1UTXZl0xmLRwgh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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f96e6b4dba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the separate and pooled models\n",
    "fig, axes = plt.subplots(2, 1, sharex=True, figsize=(8, 8))\n",
    "x = np.linspace(0, 1, 250)\n",
    "\n",
    "# separate\n",
    "ax = axes[0]\n",
    "lines = ax.plot(\n",
    "    x,\n",
    "    beta.pdf(x[:,None], y[:-1] + 1, n[:-1] - y[:-1] + 1),\n",
    "    color='C0',\n",
    "    linewidth=0.5\n",
    ")\n",
    "# highlight the last line\n",
    "lines[-1].set_linewidth(2)\n",
    "lines[-1].set_color('r')\n",
    "ax.legend(\n",
    "    (lines[0], lines[-1]),\n",
    "    (r'Posterior of $\\theta_j$',\n",
    "     r'Posterior of $\\theta_{71}$')\n",
    ")\n",
    "ax.set_ylim((0, ax.set_ylim()[1]))  # set y base to zero\n",
    "ax.set_yticks(())\n",
    "ax.set_title('separate model')\n",
    "\n",
    "# pooled\n",
    "ax = axes[1]\n",
    "ax.plot(\n",
    "    x,\n",
    "    beta.pdf(x, y.sum() + 1, n.sum() - y.sum() + 1),\n",
    "    linewidth=2,\n",
    "    label=(r'Posterior of common $\\theta$')\n",
    ")\n",
    "ax.legend()\n",
    "ax.set_ylim((0, ax.set_ylim()[1]))  # set y base to zero\n",
    "ax.set_yticks(())\n",
    "ax.set_xlabel(r'$\\theta$')\n",
    "ax.set_title('pooled model')\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# compute the marginal posterior of alpha and beta in the hierarchical model in a grid\n",
    "A = np.linspace(0.5, 6, 100)\n",
    "B = np.linspace(3, 33, 100)\n",
    "# calculated in logarithms for numerical accuracy\n",
    "lp = (\n",
    "  - 5/2 * np.log(A + B[:,None])\n",
    "  + np.sum(\n",
    "        gammaln(A + B[:,None])\n",
    "      - gammaln(A)\n",
    "      - gammaln(B[:,None])\n",
    "      + gammaln(A + y[:,None,None])\n",
    "      + gammaln(B[:,None] + (n - y)[:,None,None])\n",
    "      - gammaln(A + B[:,None] + n[:,None,None]),\n",
    "        axis=0\n",
    "    )\n",
    ")\n",
    "# subtract the maximum value to avoid over/underflow in exponentation\n",
    "lp -= lp.max()\n",
    "p = np.exp(lp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XrDfcm8gOul8j+6Fx52wKH7JW/BeQ9cb7Ell70UnAs0MIB2azrdybgA8C/5fsIHQpWSeH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\n3ErqGQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f96e48c4e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the marginal posterior\n",
    "plt.imshow(\n",
    "    p,\n",
    "    origin='lower',\n",
    "    aspect='auto',\n",
    "    extent=(A[0], A[-1], B[0], B[-1])\n",
    ")\n",
    "plt.xlabel(r'$\\alpha$')\n",
    "plt.ylabel(r'$\\beta$')\n",
    "plt.title('The marginal posterior of alpha and beta in hierarchical model')\n",
    "plt.grid('off')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# sample from the posterior grid of alpha and beta\n",
    "nsamp = 1000\n",
    "samp_indices = np.unravel_index(\n",
    "    np.random.choice(p.size, size=nsamp, p=p.ravel()/p.sum()),\n",
    "    p.shape\n",
    ")\n",
    "samp_A = A[samp_indices[1]]\n",
    "samp_B = B[samp_indices[0]]\n",
    "# add random jitter, see BDA3 p. 76\n",
    "samp_A += (np.random.rand(nsamp) - 0.5) * (A[1]-A[0])\n",
    "samp_B += (np.random.rand(nsamp) - 0.5) * (B[1]-B[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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g48lOMpPMNPf6WFWWFrMDbSzrZ2eyID+Jxl4v+xr6WFSQzIObakbMh7NhdgZv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\nxcWJmZmZlYqLEzMzMysVFydmZmZWKv8DYcxg9QzpzlwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f96e48d4a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(2, 1, sharex=True, figsize=(8, 8))\n",
    "\n",
    "# Plot samples from the distribution of distributions Beta(alpha,beta),\n",
    "# that is, plot Beta(alpha,beta) using the posterior samples of alpha and beta\n",
    "ax = axes[0]\n",
    "ax.plot(\n",
    "    x,\n",
    "    beta.pdf(x[:,None], samp_A[:20], samp_B[:20]),\n",
    "    linewidth=0.5,\n",
    "    color='C0'\n",
    ")\n",
    "ax.set_yticks(())\n",
    "ax.set_title(\n",
    "    r'Posterior samples from the distribution of distributions '\n",
    "    r'Beta($\\alpha$,$\\beta$)'\n",
    ")\n",
    "ax.set_ylim((0, ax.set_ylim()[1]))  # set y base to zero\n",
    "\n",
    "# The average of above distributions, is the predictive distribution for a new\n",
    "# theta, and also the prior distribution for theta_j.\n",
    "# Plot this.\n",
    "ax = axes[1]\n",
    "plt.plot(x, np.mean(beta.pdf(x, samp_A[:,None], samp_B[:,None]), axis=0))\n",
    "ax.set_yticks(())\n",
    "ax.set_xlabel(r'$\\theta$')\n",
    "ax.set_title(\n",
    "    r'Predictive distribution for a new $\\theta$ '\n",
    "    r'and prior for $\\theta_j$'\n",
    ")\n",
    "ax.set_ylim((0, ax.set_ylim()[1]))  # set y base to zero\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Ez9We5AOyDYIQQghxuuhxgQZgaLArO7LKu7sZQgghhDhFemagCXJle7YEGiGEEOJ00TMD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\nF0c6MK07JdLIgjsyiQ7RcuM7O1idXcGgWDML78wkJ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M6Jzekh2qwjyqwlzKgl1KBpOiwG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\nJEmSJEnq8WRCI0mSJElSj/f/AQ+pDxSgycqHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f96def750f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# And finally compare the separate model and the hierarchical model\n",
    "fig, axes = plt.subplots(2, 1, sharex=True, figsize=(8, 8))\n",
    "x = np.linspace(0, 1, 250)\n",
    "\n",
    "# first plot the separate model (same as above)\n",
    "ax = axes[0]\n",
    "# note that for clarity only every 7th distribution is plotted\n",
    "lines = ax.plot(\n",
    "    x,\n",
    "    beta.pdf(x[:,None], y[7:-1:7] + 1, n[7:-1:7] - y[7:-1:7] + 1),\n",
    "    color='C0',\n",
    "    linewidth=1\n",
    ")\n",
    "# highlight the last line\n",
    "lines[-1].set_linewidth(2)\n",
    "lines[-1].set_color('r')\n",
    "ax.set_yticks(())\n",
    "ax.set_title('separate model')\n",
    "ax.set_ylim((0, ax.set_ylim()[1]))  # set y base to zero\n",
    "\n",
    "# And the hierarchical model. Note that these marginal posteriors for theta_j are\n",
    "# more narrow than in the separate model case, due to the borrowed information from\n",
    "# the other theta_j's.\n",
    "ax = axes[1]\n",
    "# note that for clarity only every 7th distribution is plotted\n",
    "lines = ax.plot(\n",
    "    x,\n",
    "    np.mean(\n",
    "        beta.pdf(\n",
    "            x[:,None],\n",
    "            y[7::7] + samp_A[:,None,None],\n",
    "            n[7::7] - y[7::7] + samp_B[:,None,None]\n",
    "        ),\n",
    "        axis=0\n",
    "    ),\n",
    "    color='C0',\n",
    "    linewidth=1,\n",
    ")\n",
    "# highlight the last line\n",
    "lines[-1].set_linewidth(2)\n",
    "lines[-1].set_color('r')\n",
    "ax.set_yticks(())\n",
    "ax.set_xlabel(r'$\\theta$')\n",
    "ax.set_title('hierarchical model')\n",
    "ax.set_ylim((0, ax.set_ylim()[1]))  # set y base to zero\n",
    "\n",
    "fig.tight_layout()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
